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Question: The set of values of x for which the expression \(\frac{\tan 3x - \tan 2x}{1 + \tan 3x\tan 2x}\) =1...

The set of values of x for which the expression

tan⁡3x−tan⁡2x1+tan⁡3xtan⁡2x\frac{\tan 3x - \tan 2x}{1 + \tan 3x\tan 2x} =1 is

A

φ\varphi

B

π4\frac{\pi}{4}

C

{nπ+π4:n=1,2,3...}\left\{ n\pi + \frac{\pi}{4}:n = 1,2,3... \right\}

D

{2nπ+π4:n=1,2,3...}\left\{ 2n\pi + \frac{\pi}{4}:n = 1,2,3... \right\}

Answer

φ\varphi

Explanation

Solution

tan⁡(3x−2x)=tan⁡x=1⇒x=nπ+π4.\tan(3x - 2x) = \tan x = 1 \Rightarrow x = n\pi + \frac{\pi}{4}. But this value does not satisfy the given equation.